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- ひでか えいさか
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2 Li-Yao,, Li-Yao The Life-Cycle Effects of House Price Changes (Li-Yao ),,,, ( ) 1 ω ( ) ω 1 γ Ct Ht t T βt U(C t, H t, N t) = N t N t t T βt N t 1 γ H t : t C t : t β : ω : γ : W. Li, R. Yao, The life-cycle effects of house price changes. Journal of Money, Credit and Banking, 39, , / 34
3 Li-Yao, ( ) 4 5 (, ) 6 3 / 34
4 ,, Li-Yao Li-Yao,, 4 / 34
5 T = {1,..., t max }, J x tj : t j ( :1, :0) y tj : t j ( :1, :0) z tj : t j ( :1, :0) c t : t s t : t x tj y tj j J x tj + j J y tj 1 t T 5 / 34
6 u tj : t j ( :1, :0) v tj : t j ( :1, :0) m t : t u tj v tj j J u tj + j J v tj = 1 t T 6 / 34
7 g t : t h j : j r : r : π : u 0j : t = 0 j v 0j : t = 0 j j J u 0j + j J v 0j = 1 7 / 34
8 maximize subject to β t U c t, t T j J ( ) h j utj + v uj (1) (1 + r)s t 1 + g t c t s t (1 + r )m t 1 + m t π j J h j v tj j J h j x tj + j J h j z tj = 0 t T (2) m t h j u tj j J t T (3) z tj u (t 1)j t T, j J (4) z tj u (t 1)j + x tj + y tj 1 j J j J t T, j J (5) z tj x tj + y tj t T, j J (6) j J j J x tj + y tj 1 t T (7) j J j J 8 / 34
9 u tj x tj t T, j J (8) u tj u (t 1)j j J y tj j J x tj t T, j J (9) v tj y tj t T, j J (10) v tj v (t 1)j x tj y tj j J j J t T, j J (11) u tj + v tj = 1 j J j J t T (12) m tmax = 0 (13) c t, s t, m t 0 t T (14) x tj, y tj, u tj, v tj, z tj {0, 1} t T, j J (15) 9 / 34
10 t T βt U(C t, H t, N t ) = t T βt N t ( Ct N t ) 1 ω ( ) ω Ht 1 γ, t T, , N t 1 γ 10 / 34
11 , 2 1 2,, 1, 2 2, 1, 1 11 / 34
12 : Numerical Optimizer(18.1.0), 12 / 34
13 T 10 J 4 s 0 1 g 1,..., g h h h h 4 9 r r π β m / 34
14 : ( : ) v0_1 Figure:,, x1_4 = 1 u1_4 x2_4 = 1 u2_4 x3_4 = 1 u3_4 u4_4 x5_4 = 1 u6_4 u7_4 u8_4 x9_4 = 1 u9_4 y10_4 = 1, z10_4 = 1 v10_4 t c t s t m t / 34
15 : ( : ) v0_4 Figure:,, x1_4 = 1 u6_4 u1_4 x2_4 = 1, z2_4 = 1 u7_4 u2_4 u8_4 u3_4 u9_4 u4_4 y10_4 = 1, z10_4 = 1 v10_4 t c t s t m t / 34
16 : ( : ) u0_1 x1_4 = 1 x6_4 = 1, z6_4 = 1 u1_4 u6_4 u7_4 u2_4 x8_4 = 1, z8_4 = 1 x3_4 = 1, z3_4 = 1 u8_4 u3_4 x9_4 = 1, z9_4 = 1 u9_4 u4_4 y10_4 = 1, z10_4 = 1 v10_4 Figure:,, t c t s t m t / 34
17 : ( : ) u0_4 x1_4 = 1 u6_4 u1_4 x2_4 = 1, z2_4 = 1 u7_4 u2_4 x8_4 = 1, z8_4 = 1 x3_4 = 1, z3_4 = 1 u8_4 u3_4 x9_4 = 1, z9_4 = 1 x4_4 = 1, z4_4 = 1 u9_4 u4_4 y10_4 = 1, z10_4 = 1 v10_4 Figure:,, t c t s t m t / 34
18 u0_1 x1_4 = 1 x6_4 = 1, z6_4 = 1 u1_4 u6_4 u7_4 u2_4 x8_4 = 1, z8_4 = 1 x3_4 = 1, z3_4 = 1 u8_4 u3_4 x9_4 = 1, z9_4 = 1 u9_4 u4_4, y10_4 = 1, z10_4 = 1 v10_4 18 / 34
19 (1 + r)s t 1 + g t c t s t (1 + r )m t 1 + m t π j J h j v tj (1 + }{{} δ ) j J h j x tj + j J h j z tj = 0 δ : 19 / 34
20 T 10 J 4 s 0 1 g 1,..., g h h h h 4 9 r r π β δ m / 34
21 : ( : ) v0_1 x1_4 = 1 Figure:,, u1_4 u2_4 u3_4 u4_4 u6_4 u7_4 u8_4 u9_4 y10_4 = 1, z10_4 = 1 v10_4 t c t s t m t / 34
22 : ( : ) v0_4 x1_4 = 1 Figure:,, u1_4 u2_4 u3_4 u4_4 u6_4 u7_4 u8_4 u9_4 y10_4 = 1, z10_4 = 1 v10_4 t c t s t m t / 34
23 : ( : ) u0_1 Figure:,, x1_4 = 1, z1_1 = 1 u6_4 u1_4 u7_4 u2_4 u8_4 u3_4 u9_4 u4_4 y10_4 = 1, z10_4 = 1 v10_4 t c t s t m t / 34
24 : ( : ) u0_4 Figure:,, u1_4 u2_4 u3_4 u4_4 u6_4 u7_4 u8_4 u9_4 y10_4 = 1, z10_4 = 1 v10_4 t c t s t m t / 34
25 2 u0_1 x1_4 = 1, z1_1 = 1 u1_4 u2_4 u3_4 u4_4 u6_4 u7_4 u8_4 u9_4 y10_4 = 1, z10_4 = 1, v10_4 25 / 34
26 , 1 10 m t m t j J h j u tj + M j J x tj M : M 26 / 34
27 T 10 J 4 s 0 1 g 1,..., g h h h h 4 9 r r π β δ m / 34
28 : ( : ) v0_1 x1_4 = 1 u6_4 u1_4 x7_4 = 1, z7_4 = 1 u2_4 u7_4 x3_4 = 1, z3_4 = 1 u8_4 u3_4 x9_4 = 1, z9_4 = 1 u4_4 u9_4 x5_4 = 1, z5_4 = 1y10_4 = 1, z10_4 = 1 v10_4 Figure:,, t c t s t m t / 34
29 : ( : ) v0_4 x1_4 = 1 u6_4 u1_4 x7_4 = 1, z7_4 = 1 u2_4 u7_4 x3_4 = 1, z3_4 = 1 u8_4 u3_4 x9_4 = 1, z9_4 = 1 u4_4 u9_4 x5_4 = 1, z5_4 = 1y10_4 = 1, z10_4 = 1 v10_4 Figure:,, t c t s t m t / 34
30 : ( : ) u0_1 x1_4 = 1, z1_1 = 1 u6_4 u1_4 x7_4 = 1, z7_4 = 1 u2_4 u7_4 x3_4 = 1, z3_4 = 1 u8_4 u3_4 x9_4 = 1, z9_4 = 1 u4_4 u9_4 x5_4 = 1, z5_4 = 1y10_4 = 1, z10_4 = 1 v10_4 Figure:,, t c t s t m t / 34
31 : ( : ) u0_4 x1_4 = 1, z1_4 = 1 u6_4 u1_4 x7_4 = 1, z7_4 = 1 u2_4 u7_4 x3_4 = 1, z3_4 = 1 u8_4 u3_4 x9_4 = 1, z9_4 = 1 u4_4 u9_4 x5_4 = 1, z5_4 = 1y10_4 = 1, z10_4 = 1 v10_4 Figure:,, t c t s t m t / 34
32 3,,,,,,, 32 / 34
33 Li,Yao 2,, t = 1 t = 9,,,,, 33 / 34
34 , ( ) / 34
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1 1 22 1 x 3 (mod ) 2 2.1 ( )., b, m Z b m b (mod m) b m 2.2 (Z/mZ). = {x x (mod m)} Z m 0, 1... m 1 Z/mZ = {0, 1... m 1} + b = + b, b = b Z/mZ 1 1 Z Q R Z/Z 2.3 ( ). m {x 0, x 1,..., x m 1 } modm 2.4
ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.
24(2012) (1 C106) 4 11 (2 C206) 4 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 (). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5... 6.. 7.,,. 8.,. 1. (75%)
zz + 3i(z z) + 5 = 0 + i z + i = z 2i z z z y zz + 3i (z z) + 5 = 0 (z 3i) (z + 3i) = 9 5 = 4 z 3i = 2 (3i) zz i (z z) + 1 = a 2 {
04 zz + iz z) + 5 = 0 + i z + i = z i z z z 970 0 y zz + i z z) + 5 = 0 z i) z + i) = 9 5 = 4 z i = i) zz i z z) + = a {zz + i z z) + 4} a ) zz + a + ) z z) + 4a = 0 4a a = 5 a = x i) i) : c Darumafactory
2 G(k) e ikx = (ik) n x n n! n=0 (k ) ( ) X n = ( i) n n k n G(k) k=0 F (k) ln G(k) = ln e ikx n κ n F (k) = F (k) (ik) n n= n! κ n κ n = ( i) n n k n
. X {x, x 2, x 3,... x n } X X {, 2, 3, 4, 5, 6} X x i P i. 0 P i 2. n P i = 3. P (i ω) = i ω P i P 3 {x, x 2, x 3,... x n } ω P i = 6 X f(x) f(x) X n n f(x i )P i n x n i P i X n 2 G(k) e ikx = (ik) n
nsg02-13/ky045059301600033210
φ φ φ φ κ κ α α μ μ α α μ χ et al Neurosci. Res. Trpv J Physiol μ μ α α α β in vivo β β β β β β β β in vitro β γ μ δ μδ δ δ α θ α θ α In Biomechanics at Micro- and Nanoscale Levels, Volume I W W v W
21 2 26 i 1 1 1.1............................ 1 1.2............................ 3 2 9 2.1................... 9 2.2.......... 9 2.3................... 11 2.4....................... 12 3 15 3.1..........
